I implemented a rather simple SPH simulation using a cubic-spline-kernel and a simple non-iterative pressure solver as described in this PDF in equation 9. I followed algorithm 1 of that paper (including gravity).
The resulting particle behaviour is certainly fluid-like (with quite some compressibility as is expected from such a simple pressure solver). However as you can see in this screenshot the particles are not evenly spread when in equilibrium, but instead arrange into small clusters of about 3 particle.
Is this normal behaviour ? It appears strange to me, so I wanted to make sure this is either correct or someone would have an idea what could be wrong here.
The screenshot shows the so-called pairing instability, which is one of the most frequent instability problems in SPH computations.
Pairing instability is the consequence of the application of bell-shaped kernel functions with too large smoothing radii. Since polynomial kernel functions of at least third order have an infection point, particles, which are getting too close to each other, experience lower and lower repulsive forces and gradually stick together. This can be overcome by choosing a suitable smoothing radius leading to a rather optimal number of neighbors, which depends on the applied kernel function but usually is around 25 in 2D.
You can read about the pairing instability and other issues of SPH simulations here. Pairing instability is briefly discussed on page 9.
